Thousands of Californians who couldn’t sign up for a health care plan by 11:59 p.m. Monday because of the state insurance exchange’s sluggish website are getting a second chance to do so.

And they have until April 15.

There’s only one catch: They must attest that they had tried to apply online by the deadline, either to a certified insurance agent, enrollment counselor, call-center operator or county social worker who will help them complete their applications.

But experts in human behavior say don’t bet on people telling the truth.

Since there is no real way to prove people are lying in this case, experts say, it’s naive to think that many potential enrollees won’t just take advantage of the extended deadline -- whether or not they tried to sign up in time.

“People have the ability to be dishonest as long as they can keep on thinking of themselves as good people,” said Dan Ariely, a professor of psychology and behavioral economics at Duke University.

“Think about cheating on taxes -- it’s very similar,” Ariely said. “You go have dinner with your mother-in-law, she asks you how work is going, and all of sudden you can justify it as a business expense that’s deductible.”

Unlike the federal government’s online application for health care, which includes a “button” that people can click on declaring they were “in line” when the deadline hit, Covered California won’t have any kind of formal attestation mechanism, Lee said.

“People could say the government has been incompetent, so I couldn’t sign up,” Ariely said.

David Magnus, a professor of biomedical ethics at Stanford University, agreed.

But “the bigger issue is the failure to have the logistics worked out so more people would sign up in a smooth manner,” he said of the rocky online rollout of the health care law.

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Hank Greely, a Stanford University Law School professor, said some people will probably lie.

How many, he said, will depend in large part on how many people think there is a strong financial advantage for them to do so.

“It will depend on how many people will think that if they have not gotten the proper coverage, they are actually going to face a real fine, which will lead to them having a strong incentive to lie,” Greely said.

Those who do not sign up for a plan by April 15 face a $95 penalty or 1 percent of their annual incomes, whichever is greater.

So if someone gets health insurance because they lied about when they applied, is that so bad?

“I don’t know how upset I’m going to be about that, or how upset Covered California should be about that,” Greely said. “Because getting more people covered is, of course, their bottom line.”

Contact Tracy Seipel at 408-920-5343. Follow her at Twitter.com/taseipel.